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<div class="title">MatrixBaseEigenvalues.h</div>  </div>
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<div class="fragment"><div class="line"><a name="l00001"></a><span class="lineno">    1</span>&#160;<span class="comment">// This file is part of Eigen, a lightweight C++ template library</span></div>
<div class="line"><a name="l00002"></a><span class="lineno">    2</span>&#160;<span class="comment">// for linear algebra.</span></div>
<div class="line"><a name="l00003"></a><span class="lineno">    3</span>&#160;<span class="comment">//</span></div>
<div class="line"><a name="l00004"></a><span class="lineno">    4</span>&#160;<span class="comment">// Copyright (C) 2008 Gael Guennebaud &lt;gael.guennebaud@inria.fr&gt;</span></div>
<div class="line"><a name="l00005"></a><span class="lineno">    5</span>&#160;<span class="comment">// Copyright (C) 2010 Jitse Niesen &lt;jitse@maths.leeds.ac.uk&gt;</span></div>
<div class="line"><a name="l00006"></a><span class="lineno">    6</span>&#160;<span class="comment">//</span></div>
<div class="line"><a name="l00007"></a><span class="lineno">    7</span>&#160;<span class="comment">// This Source Code Form is subject to the terms of the Mozilla</span></div>
<div class="line"><a name="l00008"></a><span class="lineno">    8</span>&#160;<span class="comment">// Public License v. 2.0. If a copy of the MPL was not distributed</span></div>
<div class="line"><a name="l00009"></a><span class="lineno">    9</span>&#160;<span class="comment">// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.</span></div>
<div class="line"><a name="l00010"></a><span class="lineno">   10</span>&#160; </div>
<div class="line"><a name="l00011"></a><span class="lineno">   11</span>&#160;<span class="preprocessor">#ifndef EIGEN_MATRIXBASEEIGENVALUES_H</span></div>
<div class="line"><a name="l00012"></a><span class="lineno">   12</span>&#160;<span class="preprocessor">#define EIGEN_MATRIXBASEEIGENVALUES_H</span></div>
<div class="line"><a name="l00013"></a><span class="lineno">   13</span>&#160; </div>
<div class="line"><a name="l00014"></a><span class="lineno">   14</span>&#160;<span class="preprocessor">#include &quot;./InternalHeaderCheck.h&quot;</span></div>
<div class="line"><a name="l00015"></a><span class="lineno">   15</span>&#160; </div>
<div class="line"><a name="l00016"></a><span class="lineno">   16</span>&#160;<span class="keyword">namespace </span><a class="code" href="namespaceEigen.html">Eigen</a> { </div>
<div class="line"><a name="l00017"></a><span class="lineno">   17</span>&#160; </div>
<div class="line"><a name="l00018"></a><span class="lineno">   18</span>&#160;<span class="keyword">namespace </span>internal {</div>
<div class="line"><a name="l00019"></a><span class="lineno">   19</span>&#160; </div>
<div class="line"><a name="l00020"></a><span class="lineno">   20</span>&#160;<span class="keyword">template</span>&lt;<span class="keyword">typename</span> Derived, <span class="keywordtype">bool</span> IsComplex&gt;</div>
<div class="line"><a name="l00021"></a><span class="lineno">   21</span>&#160;<span class="keyword">struct </span>eigenvalues_selector</div>
<div class="line"><a name="l00022"></a><span class="lineno">   22</span>&#160;{</div>
<div class="line"><a name="l00023"></a><span class="lineno">   23</span>&#160;  <span class="comment">// this is the implementation for the case IsComplex = true</span></div>
<div class="line"><a name="l00024"></a><span class="lineno">   24</span>&#160;  <span class="keyword">static</span> <span class="keyword">inline</span> <span class="keyword">typename</span> MatrixBase&lt;Derived&gt;::EigenvaluesReturnType <span class="keyword">const</span></div>
<div class="line"><a name="l00025"></a><span class="lineno">   25</span>&#160;  run(<span class="keyword">const</span> MatrixBase&lt;Derived&gt;&amp; m)</div>
<div class="line"><a name="l00026"></a><span class="lineno">   26</span>&#160;  {</div>
<div class="line"><a name="l00027"></a><span class="lineno">   27</span>&#160;    <span class="keyword">typedef</span> <span class="keyword">typename</span> Derived::PlainObject PlainObject;</div>
<div class="line"><a name="l00028"></a><span class="lineno">   28</span>&#160;    PlainObject m_eval(m);</div>
<div class="line"><a name="l00029"></a><span class="lineno">   29</span>&#160;    <span class="keywordflow">return</span> ComplexEigenSolver&lt;PlainObject&gt;(m_eval, <span class="keyword">false</span>).eigenvalues();</div>
<div class="line"><a name="l00030"></a><span class="lineno">   30</span>&#160;  }</div>
<div class="line"><a name="l00031"></a><span class="lineno">   31</span>&#160;};</div>
<div class="line"><a name="l00032"></a><span class="lineno">   32</span>&#160; </div>
<div class="line"><a name="l00033"></a><span class="lineno">   33</span>&#160;<span class="keyword">template</span>&lt;<span class="keyword">typename</span> Derived&gt;</div>
<div class="line"><a name="l00034"></a><span class="lineno">   34</span>&#160;<span class="keyword">struct </span>eigenvalues_selector&lt;Derived, false&gt;</div>
<div class="line"><a name="l00035"></a><span class="lineno">   35</span>&#160;{</div>
<div class="line"><a name="l00036"></a><span class="lineno">   36</span>&#160;  <span class="keyword">static</span> <span class="keyword">inline</span> <span class="keyword">typename</span> MatrixBase&lt;Derived&gt;::EigenvaluesReturnType <span class="keyword">const</span></div>
<div class="line"><a name="l00037"></a><span class="lineno">   37</span>&#160;  run(<span class="keyword">const</span> MatrixBase&lt;Derived&gt;&amp; m)</div>
<div class="line"><a name="l00038"></a><span class="lineno">   38</span>&#160;  {</div>
<div class="line"><a name="l00039"></a><span class="lineno">   39</span>&#160;    <span class="keyword">typedef</span> <span class="keyword">typename</span> Derived::PlainObject PlainObject;</div>
<div class="line"><a name="l00040"></a><span class="lineno">   40</span>&#160;    PlainObject m_eval(m);</div>
<div class="line"><a name="l00041"></a><span class="lineno">   41</span>&#160;    <span class="keywordflow">return</span> EigenSolver&lt;PlainObject&gt;(m_eval, <span class="keyword">false</span>).eigenvalues();</div>
<div class="line"><a name="l00042"></a><span class="lineno">   42</span>&#160;  }</div>
<div class="line"><a name="l00043"></a><span class="lineno">   43</span>&#160;};</div>
<div class="line"><a name="l00044"></a><span class="lineno">   44</span>&#160; </div>
<div class="line"><a name="l00045"></a><span class="lineno">   45</span>&#160;} <span class="comment">// end namespace internal</span></div>
<div class="line"><a name="l00046"></a><span class="lineno">   46</span>&#160; </div>
<div class="line"><a name="l00067"></a><span class="lineno">   67</span>&#160;<span class="keyword">template</span>&lt;<span class="keyword">typename</span> Derived&gt;</div>
<div class="line"><a name="l00068"></a><span class="lineno">   68</span>&#160;<span class="keyword">inline</span> <span class="keyword">typename</span> MatrixBase&lt;Derived&gt;::EigenvaluesReturnType</div>
<div class="line"><a name="l00069"></a><span class="lineno"><a class="line" href="classEigen_1_1MatrixBase.html#a30430fa3d5b4e74d312fd4f502ac984d">   69</a></span>&#160;<a class="code" href="classEigen_1_1MatrixBase.html#a30430fa3d5b4e74d312fd4f502ac984d">MatrixBase&lt;Derived&gt;::eigenvalues</a>()<span class="keyword"> const</span></div>
<div class="line"><a name="l00070"></a><span class="lineno">   70</span>&#160;<span class="keyword"></span>{</div>
<div class="line"><a name="l00071"></a><span class="lineno">   71</span>&#160;  <span class="keywordflow">return</span> internal::eigenvalues_selector&lt;Derived, NumTraits&lt;Scalar&gt;::IsComplex&gt;::run(derived());</div>
<div class="line"><a name="l00072"></a><span class="lineno">   72</span>&#160;}</div>
<div class="line"><a name="l00073"></a><span class="lineno">   73</span>&#160; </div>
<div class="line"><a name="l00088"></a><span class="lineno">   88</span>&#160;<span class="keyword">template</span>&lt;<span class="keyword">typename</span> MatrixType, <span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> UpLo&gt; </div>
<div class="line"><a name="l00089"></a><span class="lineno">   89</span>&#160;EIGEN_DEVICE_FUNC <span class="keyword">inline</span> <span class="keyword">typename</span> <a class="code" href="classEigen_1_1Matrix.html">SelfAdjointView&lt;MatrixType, UpLo&gt;::EigenvaluesReturnType</a></div>
<div class="line"><a name="l00090"></a><span class="lineno"><a class="line" href="classEigen_1_1SelfAdjointView.html#ad4f34424b4ea12de9bbc5623cb938b4f">   90</a></span>&#160;<a class="code" href="classEigen_1_1SelfAdjointView.html#ad4f34424b4ea12de9bbc5623cb938b4f">SelfAdjointView&lt;MatrixType, UpLo&gt;::eigenvalues</a>()<span class="keyword"> const</span></div>
<div class="line"><a name="l00091"></a><span class="lineno">   91</span>&#160;<span class="keyword"></span>{</div>
<div class="line"><a name="l00092"></a><span class="lineno">   92</span>&#160;  PlainObject thisAsMatrix(*<span class="keyword">this</span>);</div>
<div class="line"><a name="l00093"></a><span class="lineno">   93</span>&#160;  <span class="keywordflow">return</span> <a class="code" href="classEigen_1_1SelfAdjointEigenSolver.html">SelfAdjointEigenSolver&lt;PlainObject&gt;</a>(thisAsMatrix, <span class="keyword">false</span>).<a class="code" href="classEigen_1_1SelfAdjointEigenSolver.html#aaf4ed4172a517a4b9f0ab222f629e261">eigenvalues</a>();</div>
<div class="line"><a name="l00094"></a><span class="lineno">   94</span>&#160;}</div>
<div class="line"><a name="l00095"></a><span class="lineno">   95</span>&#160; </div>
<div class="line"><a name="l00096"></a><span class="lineno">   96</span>&#160; </div>
<div class="line"><a name="l00097"></a><span class="lineno">   97</span>&#160; </div>
<div class="line"><a name="l00120"></a><span class="lineno">  120</span>&#160;<span class="keyword">template</span>&lt;<span class="keyword">typename</span> Derived&gt;</div>
<div class="line"><a name="l00121"></a><span class="lineno">  121</span>&#160;<span class="keyword">inline</span> <span class="keyword">typename</span> MatrixBase&lt;Derived&gt;::RealScalar</div>
<div class="line"><a name="l00122"></a><span class="lineno"><a class="line" href="classEigen_1_1MatrixBase.html#a0ff9bc0b9bea2d0822a2bf3192783102">  122</a></span>&#160;<a class="code" href="classEigen_1_1MatrixBase.html#a0ff9bc0b9bea2d0822a2bf3192783102">MatrixBase&lt;Derived&gt;::operatorNorm</a>()<span class="keyword"> const</span></div>
<div class="line"><a name="l00123"></a><span class="lineno">  123</span>&#160;<span class="keyword"></span>{</div>
<div class="line"><a name="l00124"></a><span class="lineno">  124</span>&#160;  <span class="keyword">using</span> std::sqrt;</div>
<div class="line"><a name="l00125"></a><span class="lineno">  125</span>&#160;  <span class="keyword">typename</span> Derived::PlainObject m_eval(derived());</div>
<div class="line"><a name="l00126"></a><span class="lineno">  126</span>&#160;  <span class="comment">// FIXME if it is really guaranteed that the eigenvalues are already sorted,</span></div>
<div class="line"><a name="l00127"></a><span class="lineno">  127</span>&#160;  <span class="comment">// then we don&#39;t need to compute a maxCoeff() here, comparing the 1st and last ones is enough.</span></div>
<div class="line"><a name="l00128"></a><span class="lineno">  128</span>&#160;  <span class="keywordflow">return</span> <a class="code" href="namespaceEigen.html#af4f536e8ea56702e63088efb3706d1f0">sqrt</a>((m_eval*m_eval.adjoint())</div>
<div class="line"><a name="l00129"></a><span class="lineno">  129</span>&#160;                 .eval()</div>
<div class="line"><a name="l00130"></a><span class="lineno">  130</span>&#160;                 .template selfadjointView&lt;Lower&gt;()</div>
<div class="line"><a name="l00131"></a><span class="lineno">  131</span>&#160;                 .eigenvalues()</div>
<div class="line"><a name="l00132"></a><span class="lineno">  132</span>&#160;                 .maxCoeff()</div>
<div class="line"><a name="l00133"></a><span class="lineno">  133</span>&#160;                 );</div>
<div class="line"><a name="l00134"></a><span class="lineno">  134</span>&#160;}</div>
<div class="line"><a name="l00135"></a><span class="lineno">  135</span>&#160; </div>
<div class="line"><a name="l00151"></a><span class="lineno">  151</span>&#160;<span class="keyword">template</span>&lt;<span class="keyword">typename</span> MatrixType, <span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> UpLo&gt;</div>
<div class="line"><a name="l00152"></a><span class="lineno">  152</span>&#160;EIGEN_DEVICE_FUNC <span class="keyword">inline</span> <span class="keyword">typename</span> <a class="code" href="classEigen_1_1SelfAdjointView.html#ac68139ca586d3ffb5620caed1e51f209">SelfAdjointView&lt;MatrixType, UpLo&gt;::RealScalar</a></div>
<div class="line"><a name="l00153"></a><span class="lineno"><a class="line" href="classEigen_1_1SelfAdjointView.html#a12a7da482e31ec9c517dca92dd7bae61">  153</a></span>&#160;<a class="code" href="classEigen_1_1SelfAdjointView.html#a12a7da482e31ec9c517dca92dd7bae61">SelfAdjointView&lt;MatrixType, UpLo&gt;::operatorNorm</a>()<span class="keyword"> const</span></div>
<div class="line"><a name="l00154"></a><span class="lineno">  154</span>&#160;<span class="keyword"></span>{</div>
<div class="line"><a name="l00155"></a><span class="lineno">  155</span>&#160;  <span class="keywordflow">return</span> eigenvalues().cwiseAbs().maxCoeff();</div>
<div class="line"><a name="l00156"></a><span class="lineno">  156</span>&#160;}</div>
<div class="line"><a name="l00157"></a><span class="lineno">  157</span>&#160; </div>
<div class="line"><a name="l00158"></a><span class="lineno">  158</span>&#160;} <span class="comment">// end namespace Eigen</span></div>
<div class="line"><a name="l00159"></a><span class="lineno">  159</span>&#160; </div>
<div class="line"><a name="l00160"></a><span class="lineno">  160</span>&#160;<span class="preprocessor">#endif</span></div>
<div class="ttc" id="aclassEigen_1_1MatrixBase_html_a0ff9bc0b9bea2d0822a2bf3192783102"><div class="ttname"><a href="classEigen_1_1MatrixBase.html#a0ff9bc0b9bea2d0822a2bf3192783102">Eigen::MatrixBase::operatorNorm</a></div><div class="ttdeci">RealScalar operatorNorm() const</div><div class="ttdoc">Computes the L2 operator norm.</div><div class="ttdef"><b>Definition:</b> MatrixBaseEigenvalues.h:122</div></div>
<div class="ttc" id="aclassEigen_1_1MatrixBase_html_a30430fa3d5b4e74d312fd4f502ac984d"><div class="ttname"><a href="classEigen_1_1MatrixBase.html#a30430fa3d5b4e74d312fd4f502ac984d">Eigen::MatrixBase::eigenvalues</a></div><div class="ttdeci">EigenvaluesReturnType eigenvalues() const</div><div class="ttdoc">Computes the eigenvalues of a matrix.</div><div class="ttdef"><b>Definition:</b> MatrixBaseEigenvalues.h:69</div></div>
<div class="ttc" id="aclassEigen_1_1Matrix_html"><div class="ttname"><a href="classEigen_1_1Matrix.html">Eigen::Matrix</a></div><div class="ttdoc">The matrix class, also used for vectors and row-vectors.</div><div class="ttdef"><b>Definition:</b> Matrix.h:182</div></div>
<div class="ttc" id="aclassEigen_1_1SelfAdjointEigenSolver_html"><div class="ttname"><a href="classEigen_1_1SelfAdjointEigenSolver.html">Eigen::SelfAdjointEigenSolver</a></div><div class="ttdoc">Computes eigenvalues and eigenvectors of selfadjoint matrices.</div><div class="ttdef"><b>Definition:</b> SelfAdjointEigenSolver.h:79</div></div>
<div class="ttc" id="aclassEigen_1_1SelfAdjointEigenSolver_html_aaf4ed4172a517a4b9f0ab222f629e261"><div class="ttname"><a href="classEigen_1_1SelfAdjointEigenSolver.html#aaf4ed4172a517a4b9f0ab222f629e261">Eigen::SelfAdjointEigenSolver::eigenvalues</a></div><div class="ttdeci">const RealVectorType &amp; eigenvalues() const</div><div class="ttdoc">Returns the eigenvalues of given matrix.</div><div class="ttdef"><b>Definition:</b> SelfAdjointEigenSolver.h:302</div></div>
<div class="ttc" id="aclassEigen_1_1SelfAdjointView_html_a12a7da482e31ec9c517dca92dd7bae61"><div class="ttname"><a href="classEigen_1_1SelfAdjointView.html#a12a7da482e31ec9c517dca92dd7bae61">Eigen::SelfAdjointView::operatorNorm</a></div><div class="ttdeci">RealScalar operatorNorm() const</div><div class="ttdoc">Computes the L2 operator norm.</div><div class="ttdef"><b>Definition:</b> MatrixBaseEigenvalues.h:153</div></div>
<div class="ttc" id="aclassEigen_1_1SelfAdjointView_html_ac68139ca586d3ffb5620caed1e51f209"><div class="ttname"><a href="classEigen_1_1SelfAdjointView.html#ac68139ca586d3ffb5620caed1e51f209">Eigen::SelfAdjointView::RealScalar</a></div><div class="ttdeci">NumTraits&lt; Scalar &gt;::Real RealScalar</div><div class="ttdef"><b>Definition:</b> SelfAdjointView.h:256</div></div>
<div class="ttc" id="aclassEigen_1_1SelfAdjointView_html_ad4f34424b4ea12de9bbc5623cb938b4f"><div class="ttname"><a href="classEigen_1_1SelfAdjointView.html#ad4f34424b4ea12de9bbc5623cb938b4f">Eigen::SelfAdjointView::eigenvalues</a></div><div class="ttdeci">EigenvaluesReturnType eigenvalues() const</div><div class="ttdoc">Computes the eigenvalues of a matrix.</div><div class="ttdef"><b>Definition:</b> MatrixBaseEigenvalues.h:90</div></div>
<div class="ttc" id="anamespaceEigen_html"><div class="ttname"><a href="namespaceEigen.html">Eigen</a></div><div class="ttdoc">Namespace containing all symbols from the Eigen library.</div><div class="ttdef"><b>Definition:</b> Core:139</div></div>
<div class="ttc" id="anamespaceEigen_html_af4f536e8ea56702e63088efb3706d1f0"><div class="ttname"><a href="namespaceEigen.html#af4f536e8ea56702e63088efb3706d1f0">Eigen::sqrt</a></div><div class="ttdeci">const Eigen::CwiseUnaryOp&lt; Eigen::internal::scalar_sqrt_op&lt; typename Derived::Scalar &gt;, const Derived &gt; sqrt(const Eigen::ArrayBase&lt; Derived &gt; &amp;x)</div></div>
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